A PDE Approach for Regret Bounds Under Partial Monitoring
Abstract
In this paper, we study a learning problem in which a forecaster only observes partial information. By properly rescaling the problem, we heuristically derive a limiting PDE on Wasserstein space which characterizes the asymptotic behavior of the regret of the forecaster. Using a verification type argument, we show that the problem of obtaining regret bounds and efficient algorithms can be tackled by finding appropriate smooth sub/supersolutions of this parabolic PDE.
Cite
Text
Bayraktar et al. "A PDE Approach for Regret Bounds Under Partial Monitoring." Journal of Machine Learning Research, 2023.Markdown
[Bayraktar et al. "A PDE Approach for Regret Bounds Under Partial Monitoring." Journal of Machine Learning Research, 2023.](https://mlanthology.org/jmlr/2023/bayraktar2023jmlr-pde/)BibTeX
@article{bayraktar2023jmlr-pde,
title = {{A PDE Approach for Regret Bounds Under Partial Monitoring}},
author = {Bayraktar, Erhan and Ekren, Ibrahim and Zhang, Xin},
journal = {Journal of Machine Learning Research},
year = {2023},
pages = {1-24},
volume = {24},
url = {https://mlanthology.org/jmlr/2023/bayraktar2023jmlr-pde/}
}